抽象多项Riemann-Liouville分数阶微分方程

Abstract

Abstract:

In this paper, we investigate the following abstract multi-term fractional differential equation
D_t^αnu（t）+A_jD_t^αju(t)=AD_t^αu(t)+f(t),t∈(0,τ),
where n∈N\{1}, A and A₁,…,A_n-1 are closed linear operators on a complex Banach space E, 0≤α₁<…<α_n, 0≤α<α_n, 0<τ≤∞, f(t) is an E-valued function, and D_t^α denotes the Riemann-Liouville fractional derivative of order α ([5]). We introduce and systematically analyze several new types of k-regularized (C₁,C₂)-existence and uniqueness (propagation) families for (0.1), continuing in such a way our previous researches raised in [22, 24-25] and [34]. Plenty of various examples illustrates our abstract results.

Key words: Abstract multi-term fractional differential equations, Riemann-Liouville fractional derivatives, (a,k)-Regularized C-resolvent families, Well-posedness

CLC Number:

O175.2

Marko Kostić, Li Chenggang, Li Miao. Abstract Multi-Term Fractional Differential Equations with Riemann-Liouville Derivatives[J].Acta mathematica scientia,Series A, 2016, 36(4): 601-622.

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References

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Abstract Multi-Term Fractional Differential Equations with Riemann-Liouville Derivatives

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